When you're online, you are using a computer or other device that's connected to the Internet. If someone asks if you're online, they're wondering whether you have Internet access.
You might say, "I need to go online and check my email," or "I don't know if she's still meeting me — she hasn't been online all day." Or you could describe something that's available or readable on the Internet, like a news story, as being online. While the adjective officially describes a connection to any computer network, it's almost always used these days to mean "on the Internet." The word online has been around since 1950.